Maneuvering target sparse ISAR imaging network construction method based on Unfolding technology

Abstract

The invention discloses a maneuvering target sparse ISAR imaging network construction method based on the Unfolding technology, the network is formed by cascading a nonlinear phase compensation module based on Sinc interpolation and an ISAR image reconstruction module based on an alternating direction multiplier method (ADMM), the nonlinear phase compensation module realizes motion parameter estimation through minimizing image entropy, and the ISAR image reconstruction module realizes sparse ISAR imaging through minimizing image entropy. And then interpolation compensation of the nonlinear phase is completed. The image reconstruction module carries out hierarchical expansion based on an ADMM algorithm, strengthens the relation of iteration variables between layers, and achieves rapid and steady sparse reconstruction performance. And training the network by adopting joint optimization, and jointly optimizing network parameters. According to the method, the defect that a target usually needs to move at a constant speed in an existing ISAR imaging method under the SA condition is overcome, and high-quality imaging of the maneuvering target is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of radar data processing, and in particular to a method for constructing a sparse ISAR imaging network of a maneuvering target based on the Unfolding technology. Background Art

[0002] ISAR (Inverse Synthetic Aperture Radar) imaging technology is widely used in high-resolution imaging of non-cooperative targets in all-weather and all-time environments, and plays an important role especially in remote sensing and target recognition. In ISAR imaging, the range-Doppler (RD) algorithm is one of the basic methods for obtaining target images. However, in modern multi-functional radar systems, multiple tasks usually need to be performed simultaneously, such as target detection, tracking, and imaging, etc., which often leads to limitations in radar system resources; in addition, noise may also cause the signal-to-noise ratio of individual echoes to be too low to effectively reflect target characteristics. The above situations can be summarized as the sparse aperture (SA) problem of echoes, that is, the non-uniform sampling in the azimuth direction of radar echoes. This non-uniform sampling will have a significant impact on the imaging quality, resulting in serious grating lobes in the image based on the traditional Fourier transform.

[0003] In order to suppress the image grating lobes caused by the sparse aperture, scholars have introduced the compressed sensing technology into ISAR imaging and proposed a variety of high-quality image reconstruction methods based on sparse reconstruction, which can generally be divided into three categories: greedy pursuit methods, regularization methods based on the Lp norm, and sparse Bayesian learning (SBL) methods. Greedy pursuit methods such as matching pursuit (MP) and orthogonal matching pursuit (OMP), etc., have been proven to have good effects in many SA-ISAR applications. The Lp norm method, especially the L1 norm method, can reduce the computational complexity without significantly reducing the image quality and is widely used in practice. The sparse Bayesian learning method is executed in a statistical framework and performs image reconstruction by establishing a sparse prior probability model, and has achieved certain research results, but the computational burden is heavy, which limits its use in real-time applications.

[0004] Existing SA-ISAR imaging methods often rely on the assumption that the target's motion is relatively stable during the imaging time. However, in reality, the observed targets usually have complex motion states, and their echoes contain high-order phase terms, which will cause defocusing in the images obtained by the above methods and affect the image quality. Motion compensation for maneuvering targets is a major challenge in ISAR imaging research, mainly including two key points: translational motion compensation and non-uniform rotational motion compensation. Translational motion compensation often uses a two-step method, namely range alignment and initial phase correction. However, under SA conditions, due to the disruption of the phase continuity between pulses, the performance of traditional initial phase correction methods such as Phase Gradient Autofocus (PGA) usually degrades significantly and may even become inapplicable. Non-uniform rotational motion compensation methods face problems such as random data loss and Doppler frequency jumps, and traditional methods often incur large signal-to-noise ratio losses or face high computational complexity when dealing with these problems.

[0005] Therefore, how to achieve high-quality ISAR imaging under SA conditions, especially robust real-time imaging for complex moving targets, remains an urgent technical problem to be solved. Designing efficient target motion compensation methods, robust image sparse reconstruction methods, and reducing the computational burden are the core challenges in the current SA-ISAR imaging field. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for constructing a sparse ISAR imaging network for maneuvering targets based on the Unfolding technology, which overcomes the constraint that existing ISAR imaging methods under SA conditions usually require fixed target motion and can effectively eliminate the phase error caused by non-uniform rotation.

[0007] The technical solution for achieving the purpose of the present invention is as follows: A method for constructing a sparse ISAR imaging network for maneuvering targets based on the Unfolding technology, comprising the following steps:

[0008] Step 1: Obtain radar echo data and perform preprocessing and modeling on the radar echo data; the process of preprocessing the radar echo data is to perform translational motion compensation on the radar echo data, and the translational motion compensation includes: using the accumulated cross-correlation method to perform range alignment on the echo and using the eigenvector-based method to perform initial phase correction on the echo;

[0009] Step 2: Based on the echo signal model established in Step 1, use the Unfolding framework to establish a model-driven deep learning imaging algorithm and a target optimization function; the deep learning imaging algorithm includes a non-linear phase compensation algorithm and a sparse reconstruction algorithm based on compressive sensing;

[0010] Step 3: Based on the imaging algorithm established in Step 2, construct an algorithm-unrolled neural network model; the algorithm-unrolled neural network model consists of a non-linear phase compensation module, a reconstruction layer unrolled by the fast-ADMM algorithm, a denoising layer, and a Lagrange multiplier update layer in cascade; the non-linear phase compensation module is used to compensate the non-linear phase term brought by the non-uniform rotation of the target to the echo, and the reconstruction layer unrolled by the fast-ADMM algorithm, the denoising layer, and the Lagrange multiplier update layer unroll the fast-ADMM iteration process into a cascade structure of each layer of the neural network, which is used to quickly reconstruct the preprocessed undersampled echo signal into an ISAR image;

[0011] Step 4: Generate a dataset for the ISAR echo data; the label of the training set in the dataset is the RD imaging result after translational and non-uniform rotational compensation under the full-aperture condition of the ISAR echo data; the input of the training set is the sparse echo obtained by randomly sparse sampling the ISAR echo data after translational compensation of the echo;

[0012] Step 5: Determine the loss function according to the objective optimization function in Step 2 and the dataset in Step 4;

[0013] Step 6: Train the network model constructed in Step 3 based on the dataset in Step 4 and the loss function in Step 5;

[0014] Step 7: Image the processed echo based on the network model trained in Step 6.

[0015] An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the program, it implements the above-mentioned method for constructing a sparse ISAR imaging network for maneuvering targets based on the Unfolding technology.

[0016] A computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, it implements the above-mentioned method for constructing a sparse ISAR imaging network for maneuvering targets based on the Unfolding technology.

[0017] A computer program product, comprising a computer program, and when the computer program is executed by a processor, it implements the above-mentioned method for constructing a sparse ISAR imaging network for maneuvering targets based on the Unfolding technology.

[0018] Compared with the prior art, the remarkable features of the present invention are as follows: 1) The present invention proposes an effective SA-ISAR imaging network for maneuvering targets, which suppresses the influence of sparse aperture (SA) and can effectively compensate for the high-order phase caused by non-uniform rotation of the target; 2) Compared with the traditional algorithm-based unfolding network, the present invention realizes full complex-domain calculation and fully utilizes the amplitude-phase information of ISAR echoes; 3) Based on the ADMM algorithm, the present invention designs a hierarchical unfolding network, sets the Lagrangian penalty parameter and regularization coefficient in the algorithm as learnable parameters and fixes them through training, and has stronger robustness than traditional algorithms; 4) The network structure proposed by the present invention is simple, has the advantages of high scalability and low computational burden. Description of the Drawings

[0019] Figure 1 It is a flow chart of the method for constructing a sparse ISAR imaging network for maneuvering targets based on the Unfolding technology of the present invention.

[0020] Figure 2 It is a structural diagram of the algorithm unfolding network proposed by the present invention.

[0021] Figure 3 It is a labeled RD image generated after translational compensation and non-uniform rotation compensation of the full-aperture ISAR echo in Example 1.

[0022] Figure 4 It is an RD map generated after translational compensation of the sparse aperture ISAR echo in Example 1.

[0023] Figure 5 It is a reconstructed image of processing the sparse aperture ISAR echo using the traditional ADMM algorithm in Example 1.

[0024] Figure 6 It is a reconstructed image of processing the sparse aperture ISAR echo using the algorithm unfolding network proposed by the present invention in Example 1. Detailed Embodiments

[0025] Existing inverse synthetic aperture radar (ISAR) imaging methods under sparse aperture (SA) conditions usually assume that the target is in a stationary motion during the observation time, which limits their performance in practical applications. The present invention proposes an efficient and robust SA-ISAR imaging framework for maneuvering targets, which can effectively compensate for the high-order phase of the echo caused by non-uniform rotation of the target. This framework disassembles the imaging problem with multi-factor coupling into cascaded sub-problems that are easy to solve, and designs a complex-domain neural network based on Unfolding to achieve robust solution of each sub-problem. The present invention fully utilizes the complex information of ISAR echoes and has the advantages of simple and robust structure, strong scalability and small computational burden.

[0026] Combined with Figure 1, A method for constructing a sparse ISAR imaging network of maneuvering targets based on the Unfolding technique. This network can achieve high-quality ISAR image reconstruction for the sparse echo data of maneuvering targets, suppressing the defocusing caused by maneuvering motion and the grating lobe effect caused by non-uniform azimuth sampling. The method specifically includes the following steps:

[0027] Step 1: Obtain radar echo data and perform preprocessing and modeling on the echo data. The preprocessing process of the radar echo data is to perform translational compensation on the radar echo data, and the translational compensation includes: range alignment and initial phase correction. Traditional range alignment methods still work well under SA conditions. In this invention, the cumulative cross-correlation method is used to perform range alignment on the echo. In terms of initial phase correction, the eigenvector-based method has been proven to be applicable to SA echoes. In this invention, the eigenvector-based method is used to perform initial phase correction on the echo.

[0028] After completing the translational compensation, the target observation model can be represented by the turntable model. For a maneuvering target, the rotation angle θ(t) during the observation time changes non-linearly and can be modeled by the Taylor series expansion as

[0029]

[0030] where ω1 is the coefficient of the first-order term of the non-uniform rotation Taylor series expansion, and ω2 is the coefficient of the second-order term. For convenience of expression, assuming that the target is rotating with a constant acceleration, then θ(t) can be approximated as

[0031]

[0032] Let b = ω2 / ω1 be the moment of inertia.

[0033] Assume that the target is equivalent to I scatterers, and the echo signal model after translational compensation can be expressed as

[0034]

[0035] where h(m,n) is the discretized echo model, σ i is the amplitude of the i-th scattering, m represents the discrete slow-time unit, n represents the discrete range unit, P r is the pulse repetition frequency (PRF) of the radar, f s is the sampling rate of the fast time, f c is the carrier frequency, B is the bandwidth, c is the propagation speed of the radar signal, x i ,y i are the coordinates of the i-th scatterer to the rotation center.

[0036] Step 2: Based on the echo signal model established in Step 1, use the Unfolding framework to establish an algorithm-driven deep learning imaging algorithm and an objective optimization function. The imaging algorithm includes a non-linear phase compensation algorithm and a sparse reconstruction algorithm based on compressive sensing.

[0037] The non-uniform rotation of the target will introduce a non-linear phase term to the echo. The non-linear phase can be converted into a linear phase by using interpolation and resampling. Use Sinc interpolation to compensate for the high-order phase caused by target maneuvering:

[0038]

[0039] where y 2n is the nth range cell after interpolation, y 1n is the nth range cell before interpolation, T is the pulse repetition interval (PRI), and the calculation method of m res is

[0040]

[0041] where M represents the number of pulses in the fully sampled radar echo, b is the ratio of the quadratic term coefficient to the linear term coefficient in the Taylor series expansion of non-uniform rotation, assumed to be the rotation parameter. When b = 0, the model degenerates into a uniform rotation model;

[0042] The above compensation for the non-linear phase term can be further expressed in matrix form as

[0043] Y2 = S1EY1

[0044] where Y2 is the compensated matrix of M×N, Y1 is the pulse sparse matrix of M×N, E is the interpolation matrix of M×M, and S1 is the update of the undersampling matrix determined by the pulse energy after interpolation of EY1.

[0045] After non-linear phase compensation, the SA-ISAR imaging problem can be described as

[0046] Y2 = S1FX + N

[0047] where F is an M×M Fourier matrix, X is the target ISAR image matrix, and N is the noise.

[0048] Establish the target sparse aperture ISAR imaging optimization function as

[0049]

[0050] s.t. z = x

[0051] where y is the echo matrix, x is the reconstructed ISAR matrix, S1 is the undersampling matrix, λ is the regularization coefficient, ||·||2 is the L2 norm, and ||·||1 is the L1 norm;

[0052] The sparse reconstruction algorithm is solved using fast-ADMM to obtain:

[0053]

[0054] A (k+1) = A (k) + ρ(X (k+1) - Z (k+1) )

[0055] where k represents the k-th iteration,. / represents element-wise division, and Z is an auxiliary variable; A and ρ represent the Lagrange multiplier and the penalty parameter, respectively; λ represents the regularization coefficient that determines the sparsity degree of the reconstructed ISAR image; Mask is the sampling matrix of SA data, and its element values are 1 or 0 indicating whether the element is sampled or not, 1 M×N is an all-ones matrix, and S(·) is a soft-thresholding function for real-valued threshold t and complex data x:

[0056]

[0057] The entropy of the final reconstructed image is

[0058]

[0059] where sum represents the sum of all elements in the matrix. The entropy of the reconstructed image is related to the moment of inertia b. Since the entropy of the focused image is the smallest, when the estimated b is equal to the true value, the entropy reaches the global minimum. Therefore, the parameter estimation of the moment of inertia can be approximated as an optimization problem based on minimizing the image entropy:

[0060]

[0061] Step 3: Based on the imaging algorithm established in Step 2, construct an algorithm-expanded neural network model.

[0062] Traditional fast-ADMM has problems such as a long number of iteration steps and difficulty in predefining parameters. Therefore, by combining deep learning techniques, the fast alternating direction method of multipliers is expanded into a network. More information is extracted from the data through cascading between layers and preset learnable parameters to reduce the number of iterations, improve the algorithm efficiency, and simultaneously achieve the adaptive selection of iteration parameters. Since the entropy reaches the global minimum when the non-uniform rotation compensation effect is the best, the non-uniform rotation compensation part of the algorithm is expanded as a part of the network to jointly optimize the reconstructed image.

[0063] The non - linear phase compensation module in the network is obtained by expanding the Sinc interpolation function in step 2. The moment of inertia b is used as a learnable parameter. After the interpolation module compensates the input echo, the energy of each echo obtains the updated undersampled matrix through the complex - domain softmax layer. The interpolation module is the first layer in each stage of the network.

[0064] The ISAR image reconstruction module in the network is obtained by expanding the fast - ADMM algorithm. They are respectively expanded into a reconstruction layer, a denoising layer, and a Lagrange multiplier update layer. The iterative process is expanded into Figure 2 the cascaded architecture shown; let the number of iterations of the fast - ADMM algorithm be n, and the number of stages of the cascaded network is also set to n; there are 2 unknown parameters in each stage of the network, which are λ and ρ respectively; in order to obtain more degrees of freedom, the present invention assumes that the model parameters λ and ρ are different in each stage, and ρ is different in each layer, and they are learned as learnable parameters from the training data set.

[0065] Step 4: Generate a data set for the ISAR echo data. The label of the training set in the data set is the RD imaging result after translational and non - uniform rotational compensation under the full - aperture condition of the ISAR echo data. The input of the training set is the sparse echo obtained by randomly sparse sampling of the ISAR echo data after translational compensation of the echo.

[0066] Step 5: Determine the loss function according to the optimization function in step 2 and the data set in step 4. The loss function is a metric to measure the effect of the network during training. In the present invention, the loss function is composed of the mean - square error loss and the reconstructed image entropy. The mean - square error loss calculates the average of the square of the difference between the output reconstructed image and the label image. By minimizing the mean - square error loss, the model will make the reconstructed image closer to the label image during training. Its specific expression is as follows:

[0067]

[0068] where is the image reconstructed from the i - th undersampled data, is the corresponding label data image, and C is the logarithm of the reconstructed image and the corresponding label data image in this batch of data sets. represents the Frobenius norm.

[0069] Joint optimization is performed by minimizing the image entropy to estimate the target rotation parameter to ensure the compensation accuracy. Its specific expression is as follows:

[0070]

[0071] where sum represents the sum of all elements in the matrix, and ⌒ represents element - by - element multiplication. is the image reconstructed from the i-th undersampled data, and C is the logarithm of the reconstructed images and the corresponding labeled data images in this batch of datasets.

[0072] Finally, the overall loss function of the network is obtained as:

[0073]

[0074] where α and β respectively represent the weight coefficients of the corresponding loss functions.

[0075] Step 6: Based on the dataset in Step 4 and the loss function in Step 5, train the network model constructed in Step 3. Input the sparse echoes in the dataset generated in Step 4 into the network for forward propagation, calculate the loss function value, update the network parameters using the backpropagation algorithm, and iterate continuously until the loss function converges. Finally, save the trained network model.

[0076] Step 7: Image the processed echoes based on the network model trained in Step 6. Use the sparse ISAR echo data of the maneuvering target as the network input to obtain the reconstructed image. Conduct a comparative experiment using the traditional fast-ADMM algorithm with the same number of iterations as the network layers, and calculate the image entropy (ENTROPY) and peak signal-to-noise ratio (PSNR) respectively.

[0077] Embodiment

[0078] Combined with Figure 1 , a method for constructing a sparse ISAR imaging network of maneuvering targets based on the Unfolding technology, includes the following steps:

[0079] Step 1: Obtain radar echo data and preprocess and model the echo data. The preprocessing process of the radar echo data is to perform translational compensation on the radar echo data, and the translational compensation includes: range alignment and initial phase correction. The traditional range alignment method still works well under SA conditions. The present invention uses the cumulative cross-correlation method to perform range alignment on the echoes. In terms of initial phase correction, the eigenvector-based method has been proven to be applicable to SA echoes. The present invention uses the eigenvector-based method to perform initial phase correction on the echoes.

[0080] After completing the translational compensation, the target observation model can be represented by the turntable model. For a maneuvering target, the rotation angle θ(t) during the observation time changes nonlinearly and can be modeled by the Taylor series expansion as

[0081]

[0082] For the convenience of expression, assuming that the target is rotating with a constant acceleration, then θ(t) can be approximated as

[0083]

[0084] Let \(b = \omega_2 / \omega_1\) be the moment of inertia.

[0085] Assume that the target is equivalent to \(I\) scatterers. The echo signal model after translational compensation can be expressed as

[0086]

[0087] where \(h(m,n)\) is the discretized echo model, \(\sigma\) i is the amplitude of the \(i\)-th scattering, \(m\) represents the discrete slow-time unit, \(n\) represents the discrete range unit, \(P\) r is the pulse repetition frequency (PRF) of the radar, \(f\) s is the sampling rate of the fast time, \(f\) c is the carrier frequency, \(B\) is the bandwidth, \(c\) is the propagation speed of the radar signal, \(x\) i , \(y\) i are the coordinates of the \(i\)-th scatterer to the rotation center.

[0088] Step 2: Based on the echo model established in Step 1, use the Unfolding framework to establish an algorithm-driven deep learning imaging algorithm. The imaging algorithm includes a non-linear phase compensation algorithm and a sparse reconstruction algorithm based on compressive sensing.

[0089] The non-uniform rotation of the target will introduce a non-linear phase term to the echo. The non-linear phase can be converted into a linear phase by using interpolation and resampling. Use Sinc interpolation to compensate for the high-order phase caused by target maneuver:

[0090]

[0091] where \(y\) 2n is the \(n\)-th range cell after interpolation, \(y\) 1n is the \(n\)-th range cell before interpolation, \(T\) is the pulse repetition interval (PRI), and the calculation method of \(m\) res is

[0092]

[0093] where \(M\) represents the number of pulses in the fully sampled radar echo. When \(b = 0\), the model degenerates into a uniform rotation model;

[0094] The above compensation for the non-linear phase term can be further expressed in matrix form as

[0095] \(Y_2 = S_1 E Y_1\)

[0096] Among them, Y2 is the compensated matrix of M×N, Y1 is the impulse sparse matrix of M×N, E is the interpolation matrix of M×M, and S1 is the update of the undersampling matrix determined by the impulse energy after interpolation of EY1.

[0097] The SA-ISAR imaging problem after non-linear phase compensation can be described as

[0098] Y2 = S1FX + N

[0099] Among them, F is an M×M Fourier matrix and N is noise.

[0100] The optimization function for target sparse aperture ISAR imaging is established as

[0101]

[0102] s.t. z = x

[0103] Among them, y is the echo matrix, x is the reconstructed ISAR matrix, S1 is the undersampling matrix, λ is the regularization coefficient, ||·||2 is the L2 norm, and ||·||1 is the L1 norm;

[0104] The sparse reconstruction algorithm is solved using fast-ADMM to obtain:

[0105]

[0106] A (k+1) = A (k) + ρ(X (k+1) - Z (k+1) )

[0107] Among them, k represents the k-th iteration,. / represents element-wise division, and Z is an auxiliary variable; A and ρ represent the Lagrange multiplier and the penalty parameter respectively; λ represents the regularization coefficient that determines the sparsity degree of the reconstructed ISAR image; Mask is the sampling matrix of SA data, and its element values are 1 or 0 indicating whether the element is sampled or not, 1 M×N is a matrix of all 1s, and S(·) is a soft threshold function for real-valued threshold t and complex data x:

[0108]

[0109] The entropy of the final reconstructed image is

[0110]

[0111] Among them, sum represents the sum of all elements in the matrix. The entropy of the reconstructed image is related to the moment of inertia b. Since the entropy of the focused image is the smallest, when the estimated b is equal to the true value, the entropy reaches the global minimum. Therefore, the parameter estimation of the moment of inertia can be approximated as an optimization problem based on minimizing the image entropy:

[0112]

[0113] Step 3: Based on the imaging algorithm established in Step 2, construct an algorithm-expanded neural network model.

[0114] Traditional fast-ADMM has problems such as long iteration steps and difficulty in predefined parameters. Therefore, by combining deep learning techniques, the fast alternating direction method of multipliers is expanded into a network. More information is extracted from the data through cascading between layers and preset learnable parameters to reduce the number of iterations, improve the algorithm efficiency, and simultaneously achieve adaptive selection of iterative parameters. For the minimum image entropy optimization problem, when the non-uniform rotation compensation effect is the best, the entropy reaches the global minimum. The algorithm part of non-uniform rotation compensation is expanded as part of the network to jointly optimize the reconstructed image.

[0115] The non-linear phase compensation module in the network is obtained by expanding the Sinc interpolation function in Step 2. Taking the moment of inertia b as a learnable parameter, after the interpolation module compensates the input echoes, the energies of each echo are obtained through the complex-domain softmax layer to obtain the updated undersampled matrix. The interpolation module serves as the first layer in each stage of the network.

[0116] The ISAR image reconstruction module in the network is obtained by expanding the fast-ADMM algorithm. They are respectively expanded into a reconstruction layer, a denoising layer, and a Lagrange multiplier update layer. Let the number of iterations of the fast-ADMM algorithm be n, and the number of stages of the cascaded network is also set to n; there are 2 unknown parameters in each stage of the network, namely λ and ρ. In order to obtain more degrees of freedom, the present invention assumes that the model parameters λ and ρ are different in each stage, and ρ is different in each layer. They are learned as learnable parameters from the training dataset. The initial values of the relevant learnable parameters are all set to 1.0.

[0117] Step 4: Generate a dataset for ISAR echo data. In this embodiment, an aircraft model consisting of 250 scattering points is used as the observation target. The maneuvering target rotates around its center of gravity at an angular velocity of 0.2 rad / s and has a random additional angular acceleration. The simulated radar operates in the X-band and transmits a chirp signal. The bandwidth is 1 GHz and the PRF is 300 Hz. In addition, Gaussian noise is added and the signal-to-noise ratio of the compressed echo is set to 10 dB. First, we extracted 200 radar echo matrices. Each echo matrix has 256 pulses in the azimuth direction and 256 samples in the range direction. The original data matrix is preprocessed by a motion compensation program including range alignment and initial phase correction. Then, the data matrix is converted into an RD imaging result through FFT as the labeled data. The input to the corresponding training set is the sparse echo matrix obtained by randomly sparse sampling of the corresponding echo data. 150 are randomly selected as the training set and 50 as the test set.

[0118] Step 5: Determine the loss function according to the optimization function in Step 2 and the dataset in Step 4. The loss function is a metric for measuring the effect of the network during training. In the present invention, a loss function composed of mean squared error loss and reconstructed image entropy is adopted. The mean squared error loss calculates the average of the squared differences between the output reconstructed image and the labeled image. By minimizing the mean squared error loss, the model will make the reconstructed image closer to the labeled image during training. Its specific expression is as follows:

[0119]

[0120] where is the image reconstructed from the i-th undersampled data, is the corresponding labeled data image, and C is the logarithm of the reconstructed image and the corresponding labeled data image in this batch of datasets. represents the Frobenius norm.

[0121] Joint optimization by minimizing the image entropy is used to estimate the target rotation parameters to ensure the compensation accuracy. Its specific expression is as follows:

[0122]

[0123] where sum represents the sum of all elements in the matrix. is the image reconstructed from the i-th undersampled data, and C is the logarithm of the reconstructed image and the corresponding labeled data image in this batch of datasets.

[0124] Finally, the overall loss function of the network is:

[0125]

[0126] Among them, α and β respectively represent the weight coefficients of the corresponding loss functions. In this example, α = 1 and β = 0.01 are taken.

[0127] Step 6: Based on the dataset in Step 4, train the network model constructed in Step 4 using the loss function in Step 5. Input the sparse echoes in the dataset generated in Step 5 into the network for forward propagation, calculate the loss function value, and use the backpropagation algorithm to update the network parameters. Iterate continuously until the loss function converges, and finally save the trained network model. The specific implementation of this example is based on the PyTorch framework, using the Adam optimizer, with an Intel(R) Core(TM) i7-8750H CPU and 16GB of memory. The learning rate is set to 0.0001.

[0128] Step 7: Image the processed echoes based on the network model trained in Step 6. Use the sparse ISAR echo data as the network input to obtain the reconstructed image as Figure 6 shown. The labeled RD image corresponding to the full-aperture ISAR echo is as Figure 4 shown, the RD image corresponding to the sparse ISAR echo is as Figure 3 shown, and the reconstructed image obtained by conducting a comparative experiment using the traditional fast-ADMM algorithm with an iteration number of 9 is as Figure 5 shown.

[0129] It can be seen from the figures that affected by the random missing between pulses, the image of the traditional RD algorithm has serious main lobe broadening and sidelobe rising. The traditional fast-ADMM algorithm can suppress the side effects caused by SA. However, due to its assumption of uniform target rotation, only a defocused image can be obtained for non-uniformly rotating targets. The imaging framework we proposed is not only unaffected by SA but also can achieve focused ISAR images of maneuvering targets.

[0130] To obtain a strict evaluation of the above method, we calculate the image entropy (ENTROPY) and peak signal-to-noise ratio (PSNR) of the reconstructed images respectively. The results are shown in Table 1. Both indicators of our method are better than those of the traditional fast-ADMM algorithm.

[0131] Table 1 Comparison table of imaging quality between the present invention and the traditional fast-ADMM algorithm

[0132] Method ENTROPY PSNR fast-ADMM 7.5046 22.29dB Unfolding-Net 6.8617 31.38dB

[0133] The specific implementation examples of the present invention have been described in detail above. It should be noted that the present invention is not limited to the above specific implementation manners, and those skilled in the art can make various deformations or modifications within the scope of the claims, which does not affect the essence of the present invention.

Claims

1. A method for constructing a sparse ISAR imaging network of maneuvering targets based on the Unfolding technology, characterized in that It includes the following steps: Step 1: Obtain radar echo data, and perform preprocessing and modeling on the radar echo data; The process of preprocessing the radar echo data is to perform translational compensation on the radar echo data. The translational compensation includes: using the accumulated cross-correlation method to perform range alignment on the echo and using the eigenvector-based method to perform initial phase correction on the echo; Step 2: Based on the echo signal model established in Step 1, use the Unfolding framework to establish a model-driven deep learning imaging algorithm and an objective optimization function; the deep learning imaging algorithm includes a non-linear phase compensation algorithm and a sparse reconstruction algorithm based on compressive sensing; Step 3: Based on the imaging algorithm established in Step 2, construct an algorithm-unfolding neural network model; the algorithm-unfolding neural network model is composed of a non-linear phase compensation module, a reconstruction layer unfolded by the fast-ADMM algorithm, a denoising layer, and a Lagrange multiplier update layer in cascade; the non-linear phase compensation module is used to compensate the non-uniform rotation of the target for the non-linear phase term brought by the echo, and the reconstruction layer, denoising layer, and Lagrange multiplier update layer unfolded by the fast-ADMM algorithm unfold the fast-ADMM iteration process into a cascade structure of each layer of the neural network, which is used to quickly reconstruct the undersampled echo signal after preprocessing into an ISAR image; Step 4: Generate a data set for ISAR echo data; the label of the training set in the data set is the RD imaging result after translational and non-uniform rotational compensation under the full-aperture condition of the ISAR echo data; the input of the training set is the sparse echo obtained by randomly sparse sampling the ISAR echo data after translational compensation of the echo; Step 5: Determine the loss function according to the objective optimization function in Step 2 and the data set in Step 4; Step 6: Train the network model constructed in Step 3 based on the data set in Step 4 and the loss function in Step 5; Step 7: Perform imaging on the processed echo based on the network model trained in Step 6.

2. The method for constructing a maneuvering target sparse ISAR imaging network based on the Unfolding technology according to claim 1, wherein In Step 1, assuming that the target is equivalent to I scatterers, the echo signal model after translational compensation is expressed as: where h(m,n) is the discretized echo model, and σ i is the amplitude of the i-th scattering, m represents the pulse unit, n represents the range unit, and P r is the pulse repetition frequency of the radar, f s is the sampling rate of the fast time, f c is the carrier frequency, B is the bandwidth, c is the propagation speed of the radar signal, x i , y i are the coordinates of the i-th scattering point to the rotation center; ω1 is the coefficient of the first term of the non-uniform rotation Taylor series expansion, and ω2 is the coefficient of the second term.

3. The method for constructing a maneuvering target sparse ISAR imaging network based on the Unfolding technology according to claim 1, wherein In Step 2, the non-linear phase compensation algorithm uses Sinc interpolation to compensate the high-order phase caused by target maneuvering. The interpolation formula is where y 2n is the nth range cell after interpolation, and y 1n is the nth range cell before interpolation. T is the pulse repetition time interval, and m res is calculated as where M represents the number of pulses in the fully sampled radar echo, and b is the ratio of the quadratic term coefficient to the linear term coefficient of the non-uniform rotation Taylor series expansion, which is set as the rotation parameter. When b = 0, the model degenerates into a uniform rotation model; After non-linear phase compensation, the SA-ISAR imaging problem is described as Y2 = S1FX + Ν where F is an M×M Fourier matrix, X is the target ISAR image matrix, N is the noise, Y2 is the compensated matrix of M×N, and S1 is the update of the undersampling matrix determined by the pulse energy after interpolation.

4. The method for constructing a maneuvering target sparse ISAR imaging network based on the Unfolding technology according to claim 3, characterized in that In Step 3, the objective function for sparse aperture ISAR imaging optimization is: s.t.z = x where y is the echo matrix, x is the reconstructed ISAR matrix, S1 is the undersampling matrix, λ is the regularization coefficient, ||·||2 is the L2 norm, and ||·||1 is the L1 norm; The sparse reconstruction algorithm uses fast-ADMM to solve and obtain: A (k+1) = A (k) + ρ(X (k+1) - Z (k+1) ) where k represents the k-th iteration,. / represents element-wise division, and Z is an auxiliary variable; A and ρ represent the Lagrange multiplier and the penalty parameter, respectively; λ represents the regularization coefficient that determines the sparsity of the reconstructed ISAR image; Mask is the sampling matrix of SA data, and its element values are 1 or 0 indicating whether the element is sampled or not, and 1 M×N is a matrix of all 1s, and S(·) is a soft-thresholding function for a real-valued threshold t and complex data x: The final reconstructed image entropy is: The reconstructed image entropy is related to the moment of inertia b. Since the entropy of the focused image is the smallest, when the estimated b is equal to the true value, the entropy reaches the global minimum. Therefore, the parameter estimation of the moment of inertia can be approximated as an optimization problem based on minimizing the image entropy:

5. The method for constructing a maneuvering target sparse ISAR imaging network based on the Unfolding technology according to claim 4, wherein In step 3, the non-linear phase compensation module in the network is obtained by expanding the Sinc interpolation function in step 2. Taking the moment of inertia b as a learnable parameter, after the interpolation module compensates the input echo, the energy of each echo is used to obtain the updated undersampled matrix through the complex domain softmax layer; the interpolation module serves as the first layer of the network.

6. The method for constructing a maneuvering target sparse ISAR imaging network based on the Unfolding technology according to claim 1, characterized in that In step 5, according to the optimization function in step 2 and the data set in step 4, the loss function is determined, and the joint optimization loss function is set as: where is the image reconstructed from the i-th undersampled data, is the corresponding labeled data image, C is the number of reconstructed images and corresponding labeled data images in this batch of datasets, represents the Frobenius norm, sum represents the sum of all elements in the matrix, ⊙ represents element-wise multiplication, and α and β respectively represent the weight coefficients of the corresponding loss functions.

7. An electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method according to any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method according to any one of claims 1-6.

9. A computer program product comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1-6.

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